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Start date: 2020End date: 2026Author: search.filters.author.Salahshour, SoheilType: search.filters.itemtype.Conference Paper

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    Bivariate Jacobi polynomials for solving Volterra partial integro-differential equations with the weakly singular kernel
    (John Wiley and Sons Ltd, 2021) Sadri, Khadijeh; Hosseini, K.; Mirzazadeh, M. A.; Ahmadian, Ali; Salahshour, Soheil; Singh, Jagdev; Sadri, Khadijeh, Department of Mathematics, Islamic Azad University, Rasht Branch, Rasht, Iran; Hosseini, K., Department of Mathematics, Islamic Azad University, Rasht Branch, Rasht, Iran; Mirzazadeh, M. A., Department of Engineering Science, University of Guilan, Rasht, Iran; Ahmadian, Ali, Universiti Kebangsaan Malaysia, Bangi, Malaysia, Department of Mathematics, Yakın Doğu Üniversitesi, Nicosia, Cyprus; Salahshour, Soheil, Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey; Singh, Jagdev, Department of Mathematics, JECRC University, Jaipur, India
    An operational matrix method is implemented based on the bivariate Jacobi polynomials to attain numerical solutions of a category of Volterra weakly singular partial integro-differential equations (VWSPI-DEs). Utilizing Jacobi approximations and their integral, derivative, and pseudo-integral operational matrices along with the collocation method reduces the given VWSPI-DE to a system of algebraic equations. Diverse forms of the Jacobi polynomials are used to investigate and compare errors of obtained approximate solutions. Moreover, some error bounds are computed for the error functions. Four experimental illustrations are solved to exhibit the effectiveness and suitability of the proposed scheme. © 2021 Elsevier B.V., All rights reserved.
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    Effect of Electron’s Drift Velocity in Nonlinear Ion-Acoustic Solitons in a Negative Ion Beam Plasma
    (Springer, 2024) Kalita, Jyotishmita; Das, Ranjan Kumar; Hosseini, K.; Hinçal, Evren; Salahshour, Soheil; Manukure, S.; Ma, W.-X.; Kalita, Jyotishmita, Department of Mathematics, Gauhati University, Guwahati, India; Das, Ranjan Kumar, Department of Mathematics, Arya Vidyapeeth College, Guwahati, India; Hosseini, K., Department of Mathematics, Near East University TRNC, Mersin, Turkey, Faculty of Art and Science, University of Kyrenia, Kyrenia, Cyprus; Hinçal, Evren, Department of Mathematics, Near East University TRNC, Mersin, Turkey, Faculty of Art and Science, University of Kyrenia, Kyrenia, Cyprus; Salahshour, Soheil, Faculty of Engineering and Natural Sciences, Istanbul Okan University, Tuzla, Turkey, Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
    In the present paper, the authors have explored the existence of KdV and mKdV solitons in a collisionless and unmagnetized plasma model involving positive ion and negative ion beams together with thermal electrons. For various selections of Q′(=mb/mi, negative ion beam to positive ion mass ratio) larger and less than one, low amplitude rarefactive and compressive KdV solitons are created in the plasma under the effect of the electron’s drift velocity ve′. In two intervals of drift velocity ve′ for 0≤ve′≤26 and 26.5≤ve′≤28.5 when Q′ is less than one, the existence of the mKdV solitons is demonstrated. © 2024 Elsevier B.V., All rights reserved.